CN105021342A - Ultrasonic non-intervention pressure detection method based on information fusion of plurality of transition waveforms - Google Patents

Abstract

The invention discloses an ultrasonic non-intervention pressure detection method based on information fusion of a plurality of transition waveforms. According to the method, a critical refraction longitudinal wave, a first reflection longitudinal wave, a fourth reflection longitudinal wave and a fifth reflection longitudinal wave are selected as pressure detection waveforms; and the relation between a pressure in a container and an ultrasonic speed is derived by the use of an ultrasonic sound elasticity principle and a plate and shell theory, and then the measuring module of the relation between a time delay and the container pressure is established according to the relation between the ultrasonic speed and the time delay. Based on the idea of information fusion, a plurality of waveforms are used as detection waveforms, and under the condition that time delay measuring precision of a single ultrasonic wave is not high, the relatively high pressure detection precision can still be realized. According to the method, transmission time delays, including pressure information and temperature information, of each waveform serve as input variables of the measuring module, and there is no need to measure temperature parameters of a container wall, so that errors generated in the temperature measuring process is avoided. Verified by experiments, the method is relatively high in measuring precision.

Description

Based on the ultrasound wave non-intervention type pressure detection method of multiple converted-wave information fusion

Technical field

The invention belongs to non-intervention type technical field of pressure detection, particularly relate to a kind of ultrasound wave non-intervention type pressure detection method based on multiple converted-wave information fusion.

Background technology

Being widely used of pressure vessel, it almost relates to whole industrial circle, and closely related with daily life.Pressure vessel enormous amount, it often carries inflammable, explosive, hypertoxic or corrosive medium, has explosion hazard.Once have an accident, the disasters such as fire, poisoning, pollution are easily caused to occur.In order to avoid the generation of such security incident, most effectual way is exactly periodic inspection container, and to compressing into row monitoring in real time in pressure vessel.

By the difference of sensitive element and measuring principle, the method for traditional pressure detection generally can be divided into four classes: liquid column pressure detection method, flexible type pressure detection method, electrical distance transmitting formula pressure detection method and physical property type pressure detection method.Traditional pressure detection method great majority belong to insertion type type, often need at chamber wall perforate impulse.Therefore the following drawback of ubiquity:

1) easily cause stress to concentrate, the peak stress after perforate generally can reach 3 ~ 6 times of membrane stress, easily makes container produce crack.2) be not easy to increase interim monitoring point.3) many pressure vessels do not allow perforate.

In non-intervention type technical field of pressure detection, mainly contain following several method: 1) Strain Method, namely foil gauge or fiber grating are directly pasted onto on pressure vessel outer wall, are realized the detection of pressure by the measurement strained it.2) capacitance method, is placed in outside tube wall by electrode, changes the detection that the change in dielectric constant caused realizes pressure by measuring by pressure.3) supersonic testing method, according to behaviors such as the propagation of ultrasound wave in measured medium, reflection, transmissions, by the measurement to the ultrasound wave such as velocity of propagation, signal amplitude characteristic quantity, realizes the Non-Destructive Testing to pressure.According to the difference of ultrasound wave sensitive parameter, ultrasound platen press can be divided into again two large classes: based on the method for amplitude decay and the method based on velocity of wave change.

It is relatively simple that Strain Method, capacitance method realize principle, but all there is many drawbacks.The major drawbacks of Strain Method is: weak output signals, and antijamming capability is poor; There is plastic yield, have larger non-linear under large sstrain state; There is drift, accuracy of measurement is low.The major drawbacks of capacitance method is: specific inductive capacity is larger by the impact of media components wherein and temperature; Along with polar plate spacing increases, capacitance sharply declines, and due to pressure, to change the capacitance variation amount caused very faint, is only suitable for the measurement of pipe with small pipe diameter; Easily affect by periphery electromagnetic environment, measuring accuracy is not high.And there is following drawback based on the pressure measurement method of ultrasonic amplitude attenuation: the 1) impact of medium in reflection coefficient receptor, different media can have an impact, and therefore the method can not be general; 2) amplitude of ripple is by the impact of probe reinforcing mode, pop one's head in and need to be fixed on vessel surface by certain fixture, and the reinforcing dynamics of probe can have influence on its contact performance, affects signal amplitude, introduce interference; 3) there is measurement blind area, when container tube wall is thinner, incoming signal can overlap with reflected signal, cannot pick out real Received signal strength.

Based on the ultrasound platen press of velocity of wave change compared to the ultrasonic manometry based on amplitude attenuation, the change of the ultrasonic velocity medium influence no longer in receptor.Technician has carried out useful research in this respect, and representative achievements is as follows:

Patent of invention " nondestructive pressure testing method and device thereof based on Rayleigh surface wave " (application number: CN200410066996.2), proposes a kind of non-intervention type pressure testing method based on Rayleigh surface wave.

Patent of invention " reservoir pressure detection method and measuring system based on reflected P-wave " (application number: CN201410318440.1) proposes the measurement model of a kind of reservoir pressure detection method based on reflected P-wave and band temperature compensation.

Document " the reservoir pressure method of measuring based on critical refraction longitudinal wave and surface wave " proposes the reservoir pressure measuring method of critical refraction longitudinal wave and surface wave being carried out reference.

Above-mentioned technology path, direction of benefiting our pursuits is correct, but still exists and urgently improve, weak point perfect further.First, based on the measuring method of surface wave, critical refraction longitudinal wave and reflected P-wave, its sensitivity and precision are not high, the change of the propagation delay that pressure causes is all very little, these methods are all overly dependent upon the accuracy of single ultrasound wave latency measurement, when latency measurement precision is not high, pressure measurement accuracy is low.Secondly, in these measuring methods, the change of temperature all can cause the change of propagation delay, and influence degree specific pressure is also remarkable, and therefore, these methods all will consider the impact of temperature, needs measuring tempeature trip temperature of going forward side by side to compensate.3rd, utilize the method for two ripple references, although the impact of temperature can be reduced to a certain extent, but still temperature cannot be eliminated on the impact of measuring, and the probe owing to additionally increasing, measurement mechanism becomes complicated.

Summary of the invention

The object of the invention is the deficiency for existing non-intervention type pressure detection method, propose a kind of ultrasound wave non-intervention type pressure detection method based on multiple converted-wave information fusion.It is the thought based on information fusion, adopts multiple waveform as detection waveform, when single hyperacoustic latency measurement precision is not high, still can realize higher pressure measurement accuracy.In addition, the method utilizes the time Yanzhong of each waveform all to contain the contribution of pressure and temperature to time delay, does not comprise temperature variable, do not need measuring tempeature to realize pressure survey in measurement model.

Non-intervention type pressure detection method based on multiple converted-wave information fusion is: select critical refraction longitudinal wave L _cR, the first reflected P-wave L _re-1 ^st, the 4th reflected P-wave L _re-4 ^th, the 5th reflected P-wave L _re-5 ^thfour waveforms, as the waveform of pressure detection, set up the pressure survey model based on multiple converted-wave information fusion; When incident longitudinal wave is incident with first critical angle, there is shape transformation at ultrasonic probe and pressure vessel tube wall interface, and produce critical refraction longitudinal wave L at outer tube wall place _cRand refracted shear, critical refraction longitudinal wave L _cRbe transmitted to receiving transducer place along outer tube wall to be received; Refracted shear is propagated in pressure vessel tube wall, and reflects at inner tubal wall place, produces the first inwall reflected P-wave L _re-I1 ^stwith the first reflection wave S _re-1 ^st; According to Snell law, the first internal reflection compressional wave L _re-I1 ^streflection angle be 90 °, propagate along inner tubal wall; First reflection wave S _re-1 ^stcontinue to propagate in pressure vessel tube wall, and again reflect at outer tube wall place, produce the first reflected P-wave L _re-1 ^stwith the second reflection wave S _re-2 ^nd, the first reflected P-wave L _re-1 ^streceiving transducer is transmitted to, the second reflection wave S along outer tube wall _re-2 ^ndcontinue to propagate in pressure vessel tube wall, and again reflect at inner tubal wall place, produce the second inwall reflected P-wave L _re-I2 ^ndwith the 3rd reflection wave S _re-3 ^rd, the second inwall reflected P-wave L _re-I2 ^ndpropagate along inner tubal wall, and the 3rd reflection wave S _re-3 ^rdcontinue to propagate in pressure vessel tube wall, according to this circulation way, the shear wave propagated in pressure vessel tube wall can at outer tube wall and inner tubal wall generation multiple reflections, produce multiple reflected P-wave along inner tubal wall propagation and multiple reflected P-wave propagated along outer tube wall, the receiving transducer being fixed on outer tube wall can receive critical refraction longitudinal wave L _cR, the first reflected P-wave L _re-1 ^st, the second reflected P-wave L _re-2 ^nd, the 3rd reflected P-wave L _re-3 ^rd, the 4th reflected P-wave L _re-4 ^thultrasonic signal; The change of container inner pressure can cause critical refraction longitudinal wave L _cRchange with the velocity of wave of reflected P-wave, namely its propagation delay can change, and is easy to the principle identified according to high s/n ratio, waveform, selects the critical refraction longitudinal wave L that signal to noise ratio (S/N ratio) is higher _cR, the first reflected P-wave L _re-1 ^st, the 4th reflected P-wave L _re-4 ^th, the 5th reflected P-wave L _re-5 ^thfour waveforms are as the waveform of pressure detection.

The described pressure survey model based on multiple converted-wave information fusion is: according to ultrasonic acoustic elastic principle and Plate Theory, and the relation of velocity of wave and time delay, all has linear relationship between the propagation delay of critical refraction longitudinal wave, reflected P-wave and pressure.But because the variable quantity of propagation delay is very little, cause pressure measurement accuracy not high.Based on the thought of information fusion, using the propagation delay of critical refraction longitudinal wave and reflected P-wave all as input variable, the pressure survey model based on multiple converted-wave can be obtained:

$p=A_0\·t_{L_{CR}}^{(p,\mathrm{\Δ}T)}+A_1\·t_{Lre-1}^{(p,\mathrm{\Δ}T)}+A_4\·t_{Lre-4}^{(p,\mathrm{\Δ}T)}+A_5\·t_{Lre-5}^{(p,\mathrm{\Δ}T)}---\left(1\right)$

Wherein, p is vessel internal pressure, be respectively critical refraction longitudinal wave L _cR, the first reflected P-wave L _re-1 ^st, the second reflected P-wave L _re-2 ^nd, the 3rd reflected P-wave L _re-3 ^rd, the 4th reflected P-wave L _re-4 ^thbe p at pressure, propagation delay when temperature rise is Δ T, A ₀, A ₁, A ₄, A ₅be respectively time delay weight coefficient.Adopt Multiple Regression Analysis Method can determine each weight coefficient.Under experimental conditions, pressure survey model can be obtained to be shown below:

$\begin{array}{c}p=0.0272{\mathrm{\Δt}}_{L_{CR}}^{\left(p,\mathrm{\Δ}T\right)}-0.1935{\mathrm{\Δt}}_{Lre-1^{st}}^{\left(p,\mathrm{\Δ}T\right)}+0.1334{\mathrm{\Δt}}_{Lre-4^{th}}^{\left(p,\mathrm{\Δ}T\right)}\\ +0.6136{\mathrm{\Δt}}_{Lre-5^{th}}^{\left(p,\mathrm{\Δ}t\right)}-0.1813\end{array}---\left(2\right).$

The present invention is compared with background technology, and the beneficial effect had is:

Based on the pressure detection method of multiple converted-wave based on the thought of information fusion, adopt multiple waveform as detection waveform, when single hyperacoustic latency measurement precision is not high, still can realize higher pressure measurement accuracy.The interior pressure of pressure vessel and temperature all can affect the velocity of wave of ultrasonic propagation, all need temperature as input variable in general pressure measurement method.Pressure detection method based on multiple converted-wave utilizes the critical refraction longitudinal wave L containing pressure information and temperature information _cR, the first reflected P-wave L _re-1 ^st, the second reflected P-wave L _re-2 ^nd, the 3rd reflected P-wave L _re-3 ^rd, the 4th reflected P-wave L _{re- 4} ^thpropagation delay as the input variable of measurement model, do not need the temperature parameter of other measuring vessel wall, avoid the error that temperature taking process produces.

Accompanying drawing explanation

Fig. 1 is the experimental system that the invention process adopts;

Fig. 2 is that ultrasound wave is with the travel path at pressure vessel tube wall during critical angle incidence

Embodiment

Non-intervention type pressure detection method based on multiple converted-wave information fusion is: select critical refraction longitudinal wave L _cR, the first reflected P-wave L _re-1 ^st, the 4th reflected P-wave L _re-4 ^th, the 5th reflected P-wave L _re-5 ^thfour waveforms, as the waveform of pressure detection, set up the pressure survey model based on multiple converted-wave information fusion; When incident longitudinal wave is incident with first critical angle, there is shape transformation at ultrasonic probe and pressure vessel tube wall interface, and produce critical refraction longitudinal wave L at outer tube wall place _cRand refracted shear, critical refraction longitudinal wave L _cRbe transmitted to receiving transducer place along outer tube wall to be received; Refracted shear is propagated in pressure vessel tube wall, and reflects at inner tubal wall place, produces the first inwall reflected P-wave L _re-I1 ^stwith the first reflection wave S _re-1 ^st; According to Snell law, the first internal reflection compressional wave L _re-I1 ^streflection angle be 90 °, propagate along inner tubal wall; First reflection wave S _re-1 ^stcontinue to propagate in pressure vessel tube wall, and again reflect at outer tube wall place, produce the first reflected P-wave L _re-1 ^stwith the second reflection wave S _re-2 ^nd, the first reflected P-wave L _re-1 ^streceiving transducer is transmitted to, the second reflection wave S along outer tube wall _re-2 ^ndcontinue to propagate in pressure vessel tube wall, and again reflect at inner tubal wall place, produce the second inwall reflected P-wave L _re-I2 ^ndwith the 3rd reflection wave S _re-3 ^rd, the second inwall reflected P-wave L _re-I2 ^ndpropagate along inner tubal wall, and the 3rd reflection wave S _re-3 ^rdcontinue to propagate in pressure vessel tube wall, according to this circulation way, the shear wave propagated in pressure vessel tube wall can at outer tube wall and inner tubal wall generation multiple reflections, produce multiple reflected P-wave along inner tubal wall propagation and multiple reflected P-wave propagated along outer tube wall, the receiving transducer being fixed on outer tube wall can receive critical refraction longitudinal wave L _cR, the first reflected P-wave L _re-1 ^st, the second reflected P-wave L _re-2 ^nd, the 3rd reflected P-wave L _re-3 ^rd, the 4th reflected P-wave L _re-4 ^thultrasonic signal; The change of container inner pressure can cause critical refraction longitudinal wave L _cRchange with the velocity of wave of reflected P-wave, namely its propagation delay can change, and is easy to the principle identified according to high s/n ratio, waveform, selects the critical refraction longitudinal wave L that signal to noise ratio (S/N ratio) is higher _cR, the first reflected P-wave L _re-1 ^st, the 4th reflected P-wave L _re-4 ^th, the 5th reflected P-wave L _re-5 ^thfour waveforms are as the waveform of pressure detection.

The described pressure survey model based on multiple converted-wave information fusion is: according to ultrasonic acoustic elastic principle and Plate Theory, and the relation of velocity of wave and time delay, all has linear relationship between the propagation delay of critical refraction longitudinal wave, reflected P-wave and pressure.But because the variable quantity of propagation delay is very little, cause pressure measurement accuracy not high.Based on the thought of information fusion, using the propagation delay of critical refraction longitudinal wave and reflected P-wave all as input variable, the pressure survey model based on multiple converted-wave can be obtained:

$p=A_0\·t_{L_{CR}}^{(p,\mathrm{\Δ}T)}+A_1\·t_{Lre-1}^{(p,\mathrm{\Δ}T)}+A_4\·t_{Lre-4}^{(p,\mathrm{\Δ}T)}+A_5\·t_{Lre-5}^{(p,\mathrm{\Δ}T)}---\left(1\right)$

Wherein, p is vessel internal pressure, be respectively critical refraction longitudinal wave L _cR, the first reflected P-wave L _re-1 ^st, the second reflected P-wave L _re-2 ^nd, the 3rd reflected P-wave L _re-3 ^rd, the 4th reflected P-wave L _re-4 ^thbe p at pressure, propagation delay when temperature rise is Δ T, A ₀, A ₁, A ₄, A ₅be respectively time delay weight coefficient.Adopt Multiple Regression Analysis Method can determine each weight coefficient.Under experimental conditions, pressure survey model can be obtained to be shown below:

$\begin{array}{c}p=0.0272{\mathrm{\Δt}}_{L_{CR}}^{\left(p,\mathrm{\Δ}T\right)}-0.1935{\mathrm{\Δt}}_{Lre-1^{st}}^{\left(p,\mathrm{\Δ}T\right)}+0.1334{\mathrm{\Δt}}_{Lre-4^{th}}^{\left(p,\mathrm{\Δ}T\right)}\\ +0.6136{\mathrm{\Δt}}_{Lre-5^{th}}^{\left(p,\mathrm{\Δ}T\right)}-0.1813\end{array}---\left(2\right).$

Embodiment:

As shown in Figure 1, ultrasound wave is produced by ultrasonic excitation device (CUT-2000A type defectoscope), and then incide the outer tube wall of pressure vessel with critical angle, its path of propagating in the tube wall of pressure vessel as shown in Figure 2.Concrete communication process is: when incident longitudinal wave is incident with first critical angle, at ultrasonic probe and pressure vessel tube wall interface, shape transformation occurs, and produce critical refraction longitudinal wave L at outer tube wall place _cRand refracted shear, critical refraction longitudinal wave L _cRbe transmitted to receiving transducer place along outer tube wall to be received; Refracted shear is propagated in pressure vessel tube wall, and reflects at inner tubal wall place, produces the first inwall reflected P-wave L _re-I1 ^stwith the first reflection wave S _re-1 ^st; According to Snell law, the first internal reflection compressional wave L _re-I1 ^streflection angle be 90 °, propagate along inner tubal wall; First reflection wave S _re-1 ^stcontinue to propagate in pressure vessel tube wall, and again reflect at outer tube wall place, produce the first reflected P-wave L _re-1 ^stwith the second reflection wave S _re-2 ^nd, the first reflected P-wave L _re-1 ^streceiving transducer is transmitted to, the second reflection wave S along outer tube wall _re-2 ^ndcontinue to propagate in pressure vessel tube wall, and again reflect at inner tubal wall place, produce the second inwall reflected P-wave L _re-I2 ^ndwith the 3rd reflection wave S _re-3 ^rd, the second inwall reflected P-wave L _re-I2 ^ndpropagate along inner tubal wall, and the 3rd reflection wave S _re-3 ^rdcontinue to propagate in pressure vessel tube wall, according to this circulation way, the shear wave propagated in pressure vessel tube wall can at outer tube wall and inner tubal wall generation multiple reflections, produce multiple reflected P-wave along inner tubal wall propagation and multiple reflected P-wave propagated along outer tube wall, the receiving transducer being fixed on outer tube wall can receive critical refraction longitudinal wave L _cR, the first reflected P-wave L _re-1 ^st, the second reflected P-wave L _re-2 ^nd, the 3rd reflected P-wave L _re-3 ^rd, the 4th reflected P-wave L _{re- 4} ^thetc. ultrasonic signal.

Propagate certain distance in chamber wall after, ultrasonic signal enters receiving transducer, is then gathered by high speed acquisition oscillograph.Experiment adopts Agilent DSOS254A type high-speed sampling oscillograph, and its sample frequency is up to 20GHz.In experiment, manually test pump changes pressure, utilizes constant temperature oven change temperature and keep temperature constant, the respective waveforms that the manometric registration of record standard, thermocouple thermometer registration and high-speed oscilloscope gather.

The waveform of high-speed sampling oscillograph collection is sent into computing machine and carries out filtering, calculate the corresponding time delay value of each waveform by cross correlation algorithm.Finally by multivariate statistical analysis, data are processed, the corresponding coefficient of Confirming model, obtain final pressure survey model.

Claims (2)

1., based on a non-intervention type pressure detection method for multiple converted-wave information fusion, it is characterized in that selecting critical refraction longitudinal wave L _cR, the first reflected P-wave L _re-1 ^st, the 4th reflected P-wave L _re-4 ^th, the 5th reflected P-wave L _re-5 ^thfour waveforms, as the waveform of pressure detection, set up the pressure survey model based on multiple converted-wave information fusion; When incident longitudinal wave is incident with first critical angle, there is shape transformation at ultrasonic probe and pressure vessel tube wall interface, and produce critical refraction longitudinal wave L at outer tube wall place _cRand refracted shear, critical refraction longitudinal wave L _cRbe transmitted to receiving transducer place along outer tube wall to be received; Refracted shear is propagated in pressure vessel tube wall, and reflects at inner tubal wall place, produces the first inwall reflected P-wave L _re-I1 ^stwith the first reflection wave S _re-1 ^st; According to Snell law, the first internal reflection compressional wave L _re-I1 ^streflection angle be 90 °, propagate along inner tubal wall; First reflection wave S _re-1 ^stcontinue to propagate in pressure vessel tube wall, and again reflect at outer tube wall place, produce the first reflected P-wave L _re-1 ^stwith the second reflection wave S _re-2 ^nd, the first reflected P-wave L _re-1 ^streceiving transducer is transmitted to, the second reflection wave S along outer tube wall _re-2 ^ndcontinue to propagate in pressure vessel tube wall, and again reflect at inner tubal wall place, produce the second inwall reflected P-wave L _re-I2 ^ndwith the 3rd reflection wave S _re-3 ^rd, the second inwall reflected P-wave L _re-I2 ^ndpropagate along inner tubal wall, and the 3rd reflection wave S _re-3 ^rdcontinue to propagate in pressure vessel tube wall, according to this circulation way, the shear wave propagated in pressure vessel tube wall can at outer tube wall and inner tubal wall generation multiple reflections, produce multiple reflected P-wave along inner tubal wall propagation and multiple reflected P-wave propagated along outer tube wall, the receiving transducer being fixed on outer tube wall can receive critical refraction longitudinal wave L _cR, the first reflected P-wave L _re-1 ^st, the second reflected P-wave L _re-2 ^nd, the 3rd reflected P-wave L _re-3 ^rd, the 4th reflected P-wave L _re-4 ^thultrasonic signal; The change of container inner pressure can cause critical refraction longitudinal wave L _cRchange with the velocity of wave of reflected P-wave, namely its propagation delay can change, and is easy to the principle identified according to high s/n ratio, waveform, selects the critical refraction longitudinal wave L that signal to noise ratio (S/N ratio) is higher _cR, the first reflected P-wave L _re-1 ^st, the 4th reflected P-wave L _re-4 ^th, the 5th reflected P-wave L _re-5 ^thfour waveforms are as the waveform of pressure detection.

2. a kind of non-intervention type pressure detection method based on multiple converted-wave information fusion according to claim 1, it is characterized in that: the described pressure survey model based on multiple converted-wave information fusion is: according to ultrasonic acoustic elastic principle and Plate Theory, and the relation of velocity of wave and time delay, all there is linear relationship between the propagation delay of critical refraction longitudinal wave, reflected P-wave and pressure.But because the variable quantity of propagation delay is very little, cause pressure measurement accuracy not high.Based on the thought of information fusion, using the propagation delay of critical refraction longitudinal wave and reflected P-wave all as input variable, the pressure survey model based on multiple converted-wave can be obtained:

$p=A_0\·t_{L_{CR}}^{(p,\mathrm{\Δ}T)}+A_1\·t_{Lre-1}^{(p,\mathrm{\Δ}T)}+A_4\·t_{Lre-4}^{(p,\mathrm{\Δ}T)}+A_5\·t_{Lre-5}^{(p,\mathrm{\Δ}T)}---\left(1\right)$

Wherein, p is vessel internal pressure, be respectively critical refraction longitudinal wave L _cR, the first reflected P-wave L _re-1 ^st, the second reflected P-wave L _re-2 ^nd, the 3rd reflected P-wave L _re-3 ^rd, the 4th reflected P-wave L _re-4 ^thbe p at pressure, propagation delay when temperature rise is Δ T, A ₀, A ₁, A ₄, A ₅be respectively time delay weight coefficient.Adopt Multiple Regression Analysis Method can determine each weight coefficient.Under experimental conditions, pressure survey model can be obtained to be shown below:

$\begin{array}{c}p=0.0272{\mathrm{\Δt}}_{L_{CR}}^{\left(p,\mathrm{\Δ}T\right)}-0.1935{\mathrm{\Δt}}_{Lre-1^{st}}^{\left(p,\mathrm{\Δ}T\right)}+0.1334{\mathrm{\Δt}}_{Lre-4^{th}}^{\left(p,\mathrm{\Δ}T\right)}\\ +0.6136{\mathrm{\Δt}}_{Lre-5^{th}}^{\left(p,\mathrm{\Δ}T\right)}-0.1813\end{array}---\left(2\right).$